Hundreds of thousands of EU nationals living in Britain could struggle to secure Home Office permission to stay in the UK after Brexit, according to migration experts.

The Oxford University-based Migration Observatory says hundreds of thousands of EU nationals could struggle to comply even with a streamlined application system for “settled status”, which will open in the second half of next year.

The migration experts say those who might find themselves excluded after Brexit include those who cannot provide the necessary evidence that they have lawfully lived in Britain for five years, those who do not apply within the time limit, and complicated cases including those who have significant but justified absences from the UK.

“Most EU citizens should have little trouble getting their status resolved if the simplified system the government has proposed goes ahead. But there are still big questions about what will happen to the minority who don’t have official evidence that they have been living in the UK,” said Madeleine Sumption, Migration Observatory’s director.

“It’s impossible to estimate exactly how many this will be. But even if it is only a few per cent of the total, the numbers of applicants affected would run into the tens or even the hundreds of thousands.”

The Migration Observatory warning follows a promise by the immigration minister, Brandon Lewis, on Tuesday that the streamlined application system for the 3 million EU nationals in Britain would include an online form of six to eight questions, cost no more than the £72 charged for a British passport and should deliver a decision within two weeks of the application being submitted.

“The way we are looking to develop this is using online processes where somebody spends literally a few minutes online and, within a couple of weeks, your settled status is dealt with and granted,” said Lewis.

“There is a presumption that they will be granted,” he told the House of Lords justice committee. “The only circumstance I can see someone not being granted settled status is if the criminal records check shows they are a criminal, or if someone was trying to claim to be an EU citizen in the UK and they were not – a fraudulent application.”

Ministers have admitted that their current system for processing applications for permanent residence from EU nationals is not fit for the purpose of registering 3 million people.

The new system will rely more on information the government already holds, including HM Revenue & Customs tax information and Department for Work and Pensions national insurance records so that those who have worked in Britain do not need to provide documents themselves.

The Migration Observatory report, The Burden of Proof, says the government is proposing to drop some of the current requirements, which have led to a 14% rejection rate in the permanent residence process. These include dropping the requirement for comprehensive sickness insurance and the test of whether work counts as “genuine and effective”.

But the migration experts say even if these changes make applying straightforward for the majority and reduce the time Home Office staff must spend reviewing each application, there will still be hundreds of thousands who are likely to struggle.

“Depending on what documentation is required, some people may not be able to meet the burden of proof. For example, people working in the cash economy and not declaring their earnings could struggle to show that they were working in the UK for five years,” says the report.

The immigration barrister Colin Yeo has pointed out that elderly people living in relative poverty who are not self-sufficient and do not have a recent work record could also be part of this group.

“Some eligible people may not apply within the proposed two-year time period, for example, because they do not realise they are required to, think they are not eligible, do not speak good enough English to navigate the process, do not have access to a computer, or have other problems such as destitution or disabilities that stand in the way,” says the report.

The Migration Observatory points out that if these people fail to apply by the deadline, they will become unlawfully resident after it expires. They could eventually face enforcement action under the Home Office’s “compliant environment” measures including detention and removal.

The third group that the experts consider may struggle with the process are those whose cases are complicated and do not meet the criteria on paper but do in practice. They cite the example of someone who might not meet the five-year residency requirement , due to significant absences from Britain, but are able to show mitigating circumstances that would need to be weighed up by a caseworker.

“The registration process for EU citizens will be prone to controversy. Any indication of fraud would be quick to hit the headlines, but if the burden of proof is high and eligible people lose their legal status, this will also undermine trust in the system,” said Sumption.